Introduction to propositional logic

Week 1

what is a proposition?

a declarative statement that is either true or false, but not both

what is a connective?

an expression that is used to modify or combine statements to make a more complex one

what does the arity of a connective mean?

the number of arguments the connective can take

different ways of expressing “if P, then Q”

Explain the truth table of “if P, then Q”

if P is true then Q MUST also be true, but if Q is true then P isn’t necessarily true

Explain the truth table of “P if and only if Q”

Conditions are equivalent and work in both directions (i.e. you can’t have one without the other)

In X→Y what is the antecedent and what is the consequent?

X is the antecedent

Y is the consequent

what is the order of precedence for logical connectives (start with highest precedence)

Negation, Conjunction, Disjunction, Implication, Equivalence

what is an interpretation / valuation ?

a function that assigns to every proportional symbol P a truth-value

what are models of the formula ?

the inputs required for the expression to evaluate to true

what is a tautology?

a formula which is true under all interpretations

what is a contradiction?

a formula which is false under all interpretations

what is a contingency?

a formula that is neither a tautology nor a contradiction

what does it mean for two formulas to be logically equivalent?

if the two formulas have the same truth-value under all interpretations

what is the logically equivalent formula of P→ Q?

¬PVQ

what is the logically equivalent form of P←>Q?

(P→Q)∧(Q→P)